Question

An automobile engine develops $100$ $kW$ when rotating at a speed of $1800rev/min$. The torque it delivers is

• A. $3.33N-m$
• B. $200N-m$
• C. $530.5N-m$
• D. $2487N-m$

Answer 1

The correct option is C $530.5N-m$

$\text{Step 1: Equation of power}$

Work done by torque is given by$;$ $W=\tau .\theta$

Differentiating with respect to time

$\Rightarrow \text{Power,}P=\frac{dW}{dt}=\tau .\frac{d\theta }{dt}=\tau .w$ $....\left(1\right)$

where $w$ is angular velocity

$\text{Step 2: Calculation of angular velocity}$

$1$ RPM $\Rightarrow \frac{2\pi }{60}rad/s$

$\Rightarrow 1800$ RPM $=\frac{2\pi }{60}\times 1800=60\pi rad/s=w$

$\text{Step 3: Calculation of power}$

From eq $....\left(1\right):$

$P=\tau .w$

$\Rightarrow 100KW=\tau \left(60\pi \right)$

$\Rightarrow \tau =\frac{100000}{60\pi }=530.5Nm$

Hence option $C$ is correct.